2. Two chemicals are mixed together and as they react the temperature of the mixture is measured. One, two and three hours after the mixing takes place, the temperatures of the chemicals are, respectively, 156.8, 161.7 and 177.2 degrees. (a) Create a system of linear equations for the data to fit the curve T(t) = at² + bt+c, where t is the time in hours and T' is the temperature. You essentially need to find a parabola that passes through the three points (1, 156.8), (2, 161.7), (3, 177.2). (b) Write the system in the form AX = b. (c) Use Cramer's Rule to solve the system. Be sure to at least show the set up for using Cramer's Rule. You can use a computer to compute the determinants if so desired. (d) Write the equation of the parabola. er

Fig: 1